1

Sample 50 points that fall within the boundaries of the city of Cologne. You will find the shapefile in the ./data folder.

The shapefile is no raster file, so that you would need the sf::read_sf() function to load the data. Sampling is straightforward: Apply the sf::st_sample to the loaded shapefile, but make sure to apply the sf::st_as_sf() function afterward to receive a full-fledged data table (with a geometry column only).

solution 

library(dplyr)

cologne <- sf::read_sf("./data/cologne.shp")

cologne_50_points <-
  cologne |>  
  sf::st_sample(50) |> 
  sf::st_as_sf()

2

Create a new raster layer comprising Cologne’s immigrant rates based on the raster layers from the previous exercises.

You would need the immigrants_cologne.tif and inhabitants_cologne.tif files in the ./data folder.

solution 

library(terra)

immigrant_rates <-
  terra::rast("./data/immigrants_cologne.tif") * 100 /
  terra::rast("./data/inhabitants_cologne.tif")

3

Extract the immigrant rate value at each position of the previously sampled points as a vector. What is your observation?

Remember that the German Census 2011 data are relatively sparse due to some severe data protection measures.

solution 

immigrant_rates_at_point <- terra::extract(immigrant_rates, cologne_50_points)

immigrant_rates_at_point
##    ID immigrants_cologne
## 1   1                 NA
## 2   2                 NA
## 3   3                 NA
## 4   4          10.377358
## 5   5                 NA
## 6   6                 NA
## 7   7                 NA
## 8   8                 NA
## 9   9                 NA
## 10 10                 NA
## 11 11                 NA
## 12 12                 NA
## 13 13                 NA
## 14 14                 NA
## 15 15                 NA
## 16 16                 NA
## 17 17                 NA
## 18 18                 NA
## 19 19                 NA
## 20 20                 NA
## 21 21                 NA
## 22 22                 NA
## 23 23                 NA
## 24 24                 NA
## 25 25                 NA
## 26 26                 NA
## 27 27                 NA
## 28 28                 NA
## 29 29                 NA
## 30 30                 NA
## 31 31                 NA
## 32 32                 NA
## 33 33           3.529412
## 34 34                 NA
## 35 35                 NA
## 36 36                 NA
## 37 37                 NA
## 38 38                 NA
## 39 39                 NA
## 40 40          17.073171
## 41 41                 NA
## 42 42                 NA
## 43 43                 NA
## 44 44                 NA
## 45 45                 NA
## 46 46                 NA
## 47 47                 NA
## 48 48          18.807339
## 49 49                 NA
## 50 50                 NA
# There are a lot of missing values.

4

Use an adequate method of raster extraction to gather information in the geographic surrounding of a point. What is your observation now?

Assume that people move in a 1,000 meters radius around their location. Thus, extracting information on buffers of 1,000 meters around the points might be interesting using the option sf::st_buffer() function. In that case, you should also set a descriptive statistics function, e.g., with the option fun = mean and its helpful companion option to consider missing values na.rm = TRUE.

solution 

immigrant_rates_1000m_buffer <-
  terra::extract(
    immigrant_rates, 
    sf::st_buffer(cologne_50_points, 1000), 
    fun = mean,
    na.rm = TRUE
    )

immigrant_rates_1000m_buffer
##    ID immigrants_cologne
## 1   1          18.258418
## 2   2                NaN
## 3   3          14.192946
## 4   4          13.767295
## 5   5          11.760282
## 6   6          27.234558
## 7   7          31.636059
## 8   8          13.165302
## 9   9                NaN
## 10 10          14.973438
## 11 11          13.162697
## 12 12          11.592882
## 13 13          14.022242
## 14 14          14.580221
## 15 15           9.827045
## 16 16          26.541320
## 17 17          48.611111
## 18 18          12.769264
## 19 19          17.705579
## 20 20          12.979616
## 21 21          13.104258
## 22 22          22.690476
## 23 23          23.877637
## 24 24          32.448624
## 25 25          12.902459
## 26 26          15.033232
## 27 27          26.306249
## 28 28          14.425409
## 29 29          17.251056
## 30 30          13.681955
## 31 31          15.557365
## 32 32          12.883983
## 33 33          14.546804
## 34 34          14.060584
## 35 35          14.040328
## 36 36          11.668190
## 37 37          13.897319
## 38 38          16.578273
## 39 39          13.719025
## 40 40          14.199787
## 41 41          17.995652
## 42 42                NaN
## 43 43          22.382594
## 44 44          19.555207
## 45 45                NaN
## 46 46           9.833143
## 47 47          27.358966
## 48 48          14.949831
## 49 49          12.528276
## 50 50          12.972539